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The graph of the equation $$y=ax^2+bx+c$$, where a, b, and c are constants, is a parabola with an axis of symmetry as $$x=-3$$. Find $$\frac{b}{a}$$ .

Feb 17, 2019

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$$\text{axis of symmetry at }x=-3 \Rightarrow\\ a(x+3)^2 + c = ax^2 + 6ax+ (9+c)\\ \dfrac{b}{a} = \dfrac{6a}{a} = 6$$

The cheater way to do it is to remember that the axis of symmetry is at

$$x = -\dfrac{b}{2a} \\ \text{so here}\\ -3 = -\dfrac{b}{2a} \\ \dfrac{b}{a} = (-3)(-2) = 6$$

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Feb 17, 2019